Solve 28=x(x+10)div2

$$28=x(x+10) \div 2$$

Solve for x

$$x=-14$$

$$x=4$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$28\times 2=x\left(x+10\right)$$

Multiply 28 and 2 to get 56.

$$56=x\left(x+10\right)$$

Use the distributive property to multiply x by x+10.

$$56=x^{2}+10x$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+10x=56$$

Subtract 56 from both sides.

$$x^{2}+10x-56=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 10 for b, and -56 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-10±\sqrt{10^{2}-4\left(-56\right)}}{2}$$

Square 10.

$$x=\frac{-10±\sqrt{100-4\left(-56\right)}}{2}$$

Multiply -4 times -56.

$$x=\frac{-10±\sqrt{100+224}}{2}$$

Add 100 to 224.

$$x=\frac{-10±\sqrt{324}}{2}$$

Take the square root of 324.

$$x=\frac{-10±18}{2}$$

Now solve the equation x=\frac{-10±18}{2} when ± is plus. Add -10 to 18.

$$x=\frac{8}{2}$$

Divide 8 by 2.

$$x=4$$

Now solve the equation x=\frac{-10±18}{2} when ± is minus. Subtract 18 from -10.

$$x=-\frac{28}{2}$$

Divide -28 by 2.

$$x=-14$$

The equation is now solved.

$$x=4 x=-14$$

Steps for Completing the Square

Multiply both sides by 2.

$$28\times 2=x\left(x+10\right)$$

Multiply 28 and 2 to get 56.

$$56=x\left(x+10\right)$$

Use the distributive property to multiply x by x+10.

$$56=x^{2}+10x$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+10x=56$$

Divide 10, the coefficient of the x term, by 2 to get 5. Then add the square of 5 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+10x+5^{2}=56+5^{2}$$

Square 5.

$$x^{2}+10x+25=56+25$$

Add 56 to 25.

$$x^{2}+10x+25=81$$

Factor x^{2}+10x+25. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+5\right)^{2}=81$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+5\right)^{2}}=\sqrt{81}$$

Simplify.

$$x+5=9 x+5=-9$$

Subtract 5 from both sides of the equation.

$$x=4 x=-14$$